Larian Studios Forums Baldur's Gate III Baldur's Gate III - Mega-threads and Guides Differences and Similarities between BG3 and D&D5e core ruleset.

This is one of those that RAW isn't super clear because Shove is only defined as a "special melee attack", so you can say you push someone with the "stick" of your polearm (like a hockey cross-check), and that should technically qualify.

However, by RAI / Sage Advice, it shouldn't work.

Jeremy Crawford ruled that shoving isn't a melee weapon attack.
https://www.sageadvice.eu/2015/07/11/are-grapple-and-shove-melee-weapon-attacks/

The Polearm Master bonus action attack triggers on "attack with only a glaive, halberd, quarterstaff, or spear" - those weapon key words implying that the bonus action is allowed when a subset of melee weapon attacks is used.